Planar field emission transistor

ABSTRACT

A field emission transistor uses carbon nanotubes positioned to extend along a substrate plane rather than perpendicularly thereto. The carbon nanotubes may be pre-manufactured and applied to the substrate and then may be etched to create a gap between the carbon nanotubes and an anode through which electrons may flow by field emission. A planar gate may be positioned beneath the gap to provide a triode structure.

CROSS REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. provisional application62/409,109 filed Oct. 17, 2016, and hereby incorporated by reference inits entirety.

BACKGROUND OF THE INVENTION

The present invention relates to transistors and specifically to a fieldemission transistor having an improved planar construction.

Vacuum tubes, such as a triode, provide for electrical amplification bycontrolling the flow of electrons in a vacuum between a cathode andanode under the influence of electrical voltage applied between thecathode and anode. Control of the electron flow is provided by means ofa grid interposed between the anode and cathode that creates anelectrical field offsetting the bias between the anode and cathode. Thegrid is normally placed near the cathode to emphasize its effect.

Vacuum tubes have been largely replaced by “solid-state” transistorsconstructed of semiconducting materials for most electricalapplications, in part, because of disadvantages of vacuum tubes withrespect to size, reliability, power consumption, and cost. Nevertheless,vacuum tubes have a number of advantages over solid-state devicesincluding very high operating frequencies, increased resistance toradiation damage, and lower noise and distortion.

Recently miniaturized vacuum tube type devices have been developedtermed “vacuum field emission transistor” (VFET). Such transistorsprovide anodes and cathodes with sharpened points in close proximity soas to promote field emissions at lower voltages and without heating ofthe cathode required in conventional vacuum tubes. Heater failure is aprimary source of vacuum tube failure and the reason for relatively highenergy consumption. The lower voltages and close proximity of the anodeand cathode also allow the transistors to operate at atmosphericpressures: low voltages ensure that the emitted electrons lack theenergy to ionize surrounding air molecules, and structure sizes smallerthan the mean free path of electrons in atmospheric pressure gas reducesthe probability of electron-molecule collisions.

A significant obstacle to the development of the VFET is the productionof small-scale sharpened anodes and cathodes that can operate for longtime periods without significant degradation from ion bombardment andthermal and mechanical stresses. Advances have been made with respect tocreating sufficiently sharpened cold cathodes through the use of carbonnanotubes, for example, as discussed in US patent application20110031867 incorporated by reference. Such systems require a carefullycontrolled synthesis step in which a carbon nanotube is grown in theproper location and orientation for the VFET, a requirement whichrepresents a significant obstacle to large-scale commercialmanufacturing.

SUMMARY OF THE INVENTION

The present invention provides a VFET structure based on carbonnanotubes applied in a planar fashion to lie along an upper surface ofan insulated substrate. The carbon nanotubes can be prefabricated usingany number of efficient fabrication processes and may be applied inoriented fashion to extend between a first and second electrode appliedto the substrate. Precise gaps between the anode and cathode electrodescan be created by selectively etching gaps in the carbon nanotubes usingconventional integrated circuit techniques.

Specifically, in one embodiment, the present invention provides a fieldemission transistor having a planar substrate with a first and secondelectrode supported by the substrate in spaced opposition across aseparation region extending along a plane of the substrate. A pluralityof carbon nanotubes are arranged in electrical communication with thefirst electrode to extend from the first electrode toward the secondelectrode terminating before the second electrode at a free space regionin the separation region. A gate electrode is placed in the free spaceregion to establish an electrical field in the free space region.Electrons may be transmitted between the first and second electrodes bya combination of electrical conduction through the plurality of carbonnanotubes and field emissions in the free space region, the lattercontrollable by the gate electrode.

It is thus a feature of at least one embodiment of the invention toprovide improved manufacturing technique for use of carbon nanotubesthat allows prefabrication of the carbon nanotubes and/or simplerplacement of the carbon nanotubes.

The plurality of carbon nanotubes may be oriented to preferentiallyextend along the direction perpendicular to an extent of the first andsecond electrodes along the planar substrate.

It is thus a feature of at least one embodiment of the invention toimprove uniformity in the transistor characteristics by controllingcarbon nanotube orientation.

The free space region for each of the plurality of carbon nanotubes maybe substantially identical.

It is thus a feature of at least one embodiment of the invention toprovide a method that can enforce a relatively constant free spaceregion for predictable transistor characteristics.

The first electrode may be a metal layer applied to the substrate overpre-applied carbon nanotubes.

It is thus a feature of at least one embodiment of the invention toprovide a simple method of connecting the carbon nanotubes to externaldevices through the use of a metallization layer applied to the carbonnanotubes.

The field emission transistor may further include an insulating materialsupported by the substrate within the separation region to provide aninsulating surface extending along the plane of the substrate to whichthe plurality of carbon nanotubes are applied.

It is thus a feature of at least one embodiment of the invention topermit application of the carbon nanotubes directly to an insulatorsimplifying fabrication and providing good planar alignment and support.

The gate may be a conductive layer extending along a plane of thesubstrate.

It is thus a feature of at least one embodiment of the invention toprovide a simple gate structure that can be readily fabricated usingintegrated circuit techniques as a layer of the integrated circuit.

The gate may be separated from the free space region by the insulatingsurface.

It is thus a feature of at least one embodiment of the invention toprevent direct contact between the gate and either of the anode orcathode of the emission transistor through the use of an interveninginsulating layer.

The field emission transistor may operate with a power supply applying anegative voltage to the first electrode for emission of electrons fromends of the plurality of carbon nanotubes. This negative voltage may bewith respect either one or both of the second electrode and the gateelectrode, representing slightly different modes of operation discussedbelow.

It is thus a feature of at least one embodiment of the invention topromote electron emission from the robust tip of the carbon nanotuberesistant to erosion.

The free space region may provide a path of field emissions extendingless than 100 nanometers.

It is thus a feature of at least one embodiment of the invention toprovide a low voltage device that can operate in vacuums or at lowpressures.

The field emissions may be between ends of the carbon nanotubes and thesecond electrode, and the second electrode is a metal electrode.

It is thus a feature of at least one embodiment of the invention toprovide a broad area anode simplifying alignment and construction of thedevice.

In one embodiment, the carbon nanotubes may extend along the substratein cantilevered fashion prior to reaching the free space region.

It is thus a feature of at least one embodiment of the invention toprovide improved field emissions that may result from removal of theends of the carbon nanotubes from the insulating surface.

The field emission transistor, in some embodiments, may include a secondplurality of carbon nanotubes in electrical communication with thesecond electrode and extending from the second electrode toward thefirst electrode to terminate at a free space region in the separationregion supported by and extending along the insulating surface towardthe first electrode without contacting the first electrode, andelectrons may be transmitted between the first and second electrodes bymeans of electrical conduction from the first electrode through thefirst plurality of carbon nanotubes and field emissions from the firstplurality of carbon nanotubes to the second plurality of carbonnanotubes and by electrical conduction from the second plurality ofcarbon nanotubes to the second electrode.

It is thus a feature of at least one embodiment of the invention toprovide carbon nanotube emitters on both electrodes, for example, forimproved field emissions shaping.

The field emission transistor may include multiple independent firstelectrodes and multiple independent second electrodes distributed overthe planar substrate to provide multiple independently controllablecircuit paths.

It is thus a feature of at least one embodiment of the invention topermit the simple fabrication of multiple devices on a planar substrateby reproduction of the structure at different locations on thesubstrate.

The invention permits an improved manufacturing process in which aplurality of carbon nanotubes may be applied to an insulating surface ofa substrate and a gap may be etched in the carbon nanotubes to define afree space region. A first electrode may be applied to the substrate inelectrical communication with the carbon nanotubes on one side of thefree space region and a second electrode applied to the substrateseparated from the carbon nanotubes in communication with the firstelectrode by the free space region. A gate electrode may be supported bythe substrate positioned to establish a controlling electrical fieldwithin the free space region

It is thus a feature of at least one embodiment of the invention toeliminate the need to precisely control the length of the carbonnanotubes or their position by etching a gap after application of thecarbon nanotubes to the substrate.

The carbon nanotubes may be prefabricated and then applied in a thinlayer to the insulating surface to be oriented to extend in asubstantially parallel fashion between the first and second electrodes.

It is thus a feature of at least one embodiment of the invention topermit prefabrication of the carbon nanotubes using techniques notreadily adaptable to growing carbon nanotubes in place on the substrate.

The etching of the gap may provide a free space region for each of theplurality of carbon nanotubes that is substantially identical.

It is thus a feature of at least one embodiment of the invention toeliminate the need to precisely position the ends of the carbonnanotubes or to carefully control their growth in place.

The first electrode may be a metal layer applied to the substrate overpre-applied carbon nanotubes.

It is thus a feature of at least one embodiment of the invention toprovide a simple method of communicating between carbon nanotubes andexternal equipment through the metallic electrode.

These particular objects and advantages may apply to only someembodiments falling within the claims and thus do not define the scopeof the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a fragmentary perspective view of the architecture of oneembodiment of the present invention showing opposed ranks of parallelnanotube cathodes and anodes as configured to create a triode;

FIG. 2 is a side elevational cross-section of the device of FIG. 1showing the path of electrons across a vacuum or low-pressure gapcontrolled by superposition of a bias field and gate field;

FIGS. 3a-g are depictions of process steps for fabricating the device ofFIG. 1;

FIG. 4 is a figure similar to FIG. 2 showing an alternative embodimentemploying a sacrificial layer to provide cantilevered ends of thecathode and anode carbon nanotubes; and

FIG. 5 is a top plan view of an alternative embodiment of the triode ofFIG. 1 using the second electrode as a continuous anode.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring now to FIG. 1, a field emission transistor 10 constructedaccording to the present invention may be fabricated on a planarsubstrate 12, for example, comprised of a layer of silicon 14 covered bya thin layer of insulating silicon dioxide 16. Such substrates arereadily available as used in the integrated circuit industry.

Attached to the upper surface of the substrate 12 are parallel ranks ofcathode carbon nanotubes 18 and anode carbon nanotubes 20 extendingparallel to a longitudinal axis 21 generally parallel to the plane ofthe upper surface of the substrate 12. In this way, the carbon nanotubes18 and 20 are supported against the upper surface of the substrate 12along their entire length. While parallel carbon nanotubes 18 arepreferred, the invention also contemplates that randomly arrayed carbonnanotubes may be used, or carbon nanotubes that are preferentiallyoriented along a single axis but not necessarily parallel.

Each cathode carbon nanotube 18 is parallel to and coaxial with acorresponding anode carbon nanotube 20 and pairs of aligned cathodecarbon nanotubes 18, and corresponding anode carbon nanotubes 20 areseparated transversely (perpendicular to the longitudinal axis 21) so asto promote field emissions separately from each cathode carbon nanotube18. Too close of a spacing reduces the field enhancement of the sharpends of the carbon nanotubes.

The pairs of aligned cathode carbon nanotubes 18 and anode carbonnanotubes 20 are separated at their distal ends by a longitudinal gap 22sized to be less than the mean free path of electrons in the environmentof the gap 22 which may either be a vacuum or gas at low or atmosphericpressure. In one embodiment, the gas may be a noble gas such as helium.The longitudinal gap 22 may be approximately 40 nanometers, for example,and typically less than 100 nanometers. An etching process removingportions of the carbon nanotubes after they have been deposited on thesubstrate 12 may provide an extremely uniform longitudinal gap 22.

Sets of the cathode carbon nanotubes 18 may be electrically joined by atransversely extending metallic bus conductor 24 at the proximal ends,for example, applied by conventional integrated circuit techniques suchas sputtering, thermal evaporation, or the like. The metallic busconductor 24, for example, may be lead, gold or other conductivematerial and will typically span multiple cathode carbon nanotubes 18 toprovide desired current flow and provides a more uniform operation byaveraging out inconsistencies from the carbon nanotube. A similarmetallic bus conductor 26 will join the proximal ends of the anodecarbon nanotubes 20 opposed to the cathode carbon nanotubes 18 joined bythe metallic bus conductor 24. The metallic bus conductor 24 provides atransistor cathode 28 of a field emission transistor according to thepresent design with the metallic bus conductor 26 providing thetransistor anode 30 of the field emission transistor 10. As depicted,multiple transistors 10, 10′ may be laid out along a common transverseaxis through the use of multiple electrically independent metallic busconductors 24 and 26 and the structure reproduced along paralleltransverse axes to create multiple devices over the surface of thesubstrate.

Referring now to FIG. 2, the silicon 14 underneath the gap 22 andunderneath the insulating silicon dioxide 16 between the cathode carbonnanotubes 18 and the anode carbon nanotubes 20 may be doped into aconductive gate region 32, for example, communicating with a gate lead34 providing a gate voltage input. The invention also contemplates thepossibility of placing a gate over the top of the carbon nanotubes 20,for example, by an adding additional layer of insulating material andattaching electrodes to the top.

This conductive gate region 32 provides the gate 36 of the fieldemission transistor 10 and will control the flow of electrons 38 betweenthe cathode carbon nanotubes 18 and the anode carbon nanotubes 20. Thepresent inventors envision one of two possible modes of operation. Inone mode, a negative voltage is applied to the cathode via a cathodelead 40 with respect to a voltage applied to the anode lead 42 toproduce a positive-going voltage gradient 43 in the gap 22 promotingfield emissions. This positive voltage gradient 43 alone will drawelectrons 38 from the cathode carbon nanotubes 18 to the anode carbonnanotubes 20 to provide electrical current. Alternatively, the fieldemissions may be created by a negative voltage on the anode lead 42 withrespect to the gate region 32.

In either case, a control voltage applied to the gate lead 34 will beused to modulate the current flowing between electrodes formed by themetallic bus conductors 24 and 26.

While the inventors do not wish to be bound by a particular theory,preliminary measurements suggest that the gate voltage can controlcurrent flow between the cathode and anode through two mechanisms: (1)by affecting field emissions in the manner of a vacuum tube and (2) byaffecting the conductivity of the nanotubes themselves through the fieldeffect (changing the number of charge carriers in the carbon nanotube).The balance between these two operating roles of affecting fieldemission of electrons and affecting nanotube conductivity can beadjusted by selecting between “metallic” carbon nanotubes andsemiconducting carbon nanotubes, the former of which would have aconductivity independent of the gate voltage. Both of these types ofcarbon nanotubes are pure carbon but have a difference in diameter andchirality of the tube as is generally understood in the art.

Referring now to FIG. 3, the fabrication of the field emissiontransistor 10 of FIG. 1 may be performed through the modification offabrication techniques used to produce carbon nanotube field effecttransistors, for example, as described in Gerald J. Brady, Austin J.Way, Nathaniel S. Safron, Harold T. Evensen, Padma Gopalan and MichaelS. Arnold, “Quasi-ballistic carbon nanotube array transistors withcurrent density exceeding Si and GaAs” Science Advances volume 02 number9, 2 Sep. 2016.

In that technique, carbon nanotubes 56, for example, commerciallyavailable from Sigma Aldrich under the trade designator 750514, may begenerated and encapsulated with PFO-BPy commercially available fromAmerican Die Source under the tradename of ADS153UV and dispersed inchloroform to develop an ink 50. As shown in FIG. 3a , the ink may beperiodically delivered in small doses (0.6-1.2 microliters) on thesurface of a water subphase 52 into which substrate 12 has been immersedand is withdrawn slowly during the deposition process. The result is toproduce a set of bands 54 of carbon nanotubes aligned perpendicular tothe longitudinal axis of withdrawal organized by the process ofdispersion of the ink on the water as adhering to the upper surface ofthe withdrawn substrate 12. Generally, the bands will be approximately100 micrometers tall (along the longitudinal axis 21) and will span theentire width of the substrate 12.

The chloroform of the ink is then evaporated producing a substrate 12having multiple carbon nanotubes 56 in parallel spaced apart andorientated along each of the bands 54 as shown in FIG. 3b . Theinvention contemplates other methods of arranging the carbon nanotubesalong the substrate including those which provide nonparallelorientations, for example, by spin casting of a slurry of dilute carbonnanotubes.

Carbon nanotubes 56 are then separated along the longitudinal axis 21 bya patterning using a protective layer 58 of polymethylmethacrylate(PMMA) applied over the surface of the carbon nanotubes 56 (shown inFIG. 3c ) and removed selectively along transverse bands 60, forexample, by electron beam lithography. The exposed regions of the carbonnanotubes 56 may then be etched with a reactive ion etching to removesegments of the carbon nanotubes 56 separating them into separate ranks62 of parallel carbon nanotubes that are apart transversely (shown inFIG. 3d ). Alternatively, this step of etching may be postponed to thefinal steps of the process after the addition of stabilizing electrodesdescribed below.

Each rank 62 may then be patterned again, (shown in FIG. 3e ) afterremoval of the protective layer 58 by acetone, with a second protectivelayer 64 exposing only the ends of the carbon nanotubes 56 of each rank62. The ends may be coated to provide for the metallic bus conductors 24and 26, for example, by thermal deposition of lead in a 30-nanometerlayer.

As shown in FIG. 3f , protective layer 64 may then be removed and, asshown in FIG. 3g , the gap 22 formed, for example, by electron beamlithography and reactive ion etching. This gap 22 may be nominally 40nanometers measured along the longitudinal axis 21 and separates thecarbon nanotubes 56 into the cathode carbon nanotubes 18 and anodecarbon nanotubes 20 described above with respect to FIG. 1. Currentlythe inventors believe that smaller gaps may be possible and beneficial.

Referring still to FIG. 3g , standard integrated circuit techniques maythen be used to provide cathode lead 40, anode lead 42, and gate lead34.

Referring now to FIG. 4, it may be possible to free the cathode carbonnanotubes 18 and anode carbon nanotubes 20 from the surface of thesubstrate 12 through the use of a sacrificial layer of material 61placed on top of the silicon dioxide layer 16 prior to the applicationof the carbon nanotubes with this material 61 removed after applicationof the metallic bus conductors 24 and 26. Removal of this materialallows the ends of the cathode carbon nanotubes 18 to extend incantilevered fashion up to the gap 22. Alternatively, channels may bepre-etched in the substrate 12 and the carbon nanotubes aligned tobridge the channels with the gap 22 cut over the channel.

It is believed that either metallic or semiconducting carbon nanotubesmay be used in this process, thereby eliminating problems ofcontamination associated with use of carbon nanotubes and field effecttransistors.

Referring now to FIG. 5, in one embodiment the gap 22 may be positionedbetween the metallic bus conductor 24 and metallic bus conductor 26 toabut metallic bus conductor 26 which may serve as a broad area anodereceiving electrons emitted from the carbon nanotubes 18. In this casethe carbon nanotubes 20 normally extending from the second metallic busconductor 26 are essentially removed by the etching process. Theconductive gate region 32 is shifted toward the metallic bus conductor26 to be positioned within the gap region controlling electron flow.

While the invention discusses parallel and aligned carbon nanotubes, theinventors also contemplate that unaligned carbon nanotubes may be used,for example, by depositing a random planar layer of overlapping carbonnanotubes and then patterning them as discussed above to provide for gap22. In this case the carbon nanotubes would not be parallel and alignedbut could still operate effectively with simplified manufacturing. Thedensity of the random planar layer would be controlled to promote thedesired spacing between ends of the carbon nanotubes at the gap 22 toenhance field emissions.

Although a planar gate construction positioned beneath the carbonnanotubes is described above, it will be appreciated that other gategeometries are possible including a gate positioned above the carbonnanotubes, or below and above the carbon nanotubes as well as a gatebeing positioned between individual or sets of carbon nanotubes orsurrounding a path of electrons from cathode to anode for individual orsets of carbon nanotubes.

Certain terminology is used herein for purposes of reference only, andthus is not intended to be limiting. For example, terms such as “upper”,“lower”, “above”, and “below” refer to directions in the drawings towhich reference is made. Terms such as “front”, “back”, “rear”, “bottom”and “side”, describe the orientation of portions of the component withina consistent but arbitrary frame of reference which is made clear byreference to the text and the associated drawings describing thecomponent under discussion. Such terminology may include the wordsspecifically mentioned above, derivatives thereof, and words of similarimport. Similarly, the terms “first”, “second” and other such numericalterms referring to structures do not imply a sequence or order unlessclearly indicated by the context.

When introducing elements or features of the present disclosure and theexemplary embodiments, the articles “a”, “an”, “the” and “said” areintended to mean that there are one or more of such elements orfeatures. The terms “comprising”, “including” and “having” are intendedto be inclusive and mean that there may be additional elements orfeatures other than those specifically noted. It is further to beunderstood that the method steps, processes, and operations describedherein are not to be construed as necessarily requiring theirperformance in the particular order discussed or illustrated, unlessspecifically identified as an order of performance. It is also to beunderstood that additional or alternative steps may be employed.

It is specifically intended that the present invention not be limited tothe embodiments and illustrations contained herein and the claims shouldbe understood to include modified forms of those embodiments includingportions of the embodiments and combinations of elements of differentembodiments as come within the scope of the following claims. All of thepublications described herein, including patents and non-patentpublications, are hereby incorporated herein by reference in theirentireties.

What we claim is:
 1. A field emission transistor comprising: a planarsubstrate; a first and second electrode supported by the substrate inspaced opposition across a separation region extending along a plane ofthe substrate; a plurality of carbon nanotubes in electricalcommunication with the first electrode and extending from the firstelectrode toward the second electrode to terminate at a free spaceregion in the separation region; and a gate electrode for establishingan electrical field in the free space region; wherein electrons may betransmitted between the first and second electrodes by a combination ofelectrical conduction through the plurality of carbon nanotubes andfield emissions in the free space region, the latter controllable by thegate electrode; wherein the first electrode is a metal layer applied tothe substrate over pre-applied carbon nanotubes.
 2. The field emissiontransistor of claim 1 wherein the plurality of carbon nanotubes areoriented to preferentially extend along a direction perpendicular to anextent of the first and second electrodes along the planar substrate. 3.The field emission transistor of claim 1 wherein the free space regionfor each of the plurality of carbon nanotubes is substantiallyidentical.
 4. The field emission transistor of claim 1 further includingan insulating material supported by the substrate within the separationregion to provide an insulating surface extending along the plane of thesubstrate to which the plurality of carbon nanotubes are applied.
 5. Thefield emission transistor of claim 1 wherein the gate is a conductivelayer extending along a plane of the substrate.
 6. The field emissiontransistor of claim/wherein the gate is separated from the free spaceregion by an insulating material.
 7. The field emission transistor ofclaim 1 further including a power supply applying a negative voltage tothe first electrode with respect to the second electrode for emission ofelectrons from ends of the plurality of carbon nanotubes.
 8. The fieldemission transistor of claim 1 wherein the free space region provides apath of field emissions extending less than 100 nanometers.
 9. The fieldemission transistor of claim 1 wherein the field emissions are betweenends of the carbon nanotubes and the second electrode and wherein thesecond electrode is a metal electrode.
 10. The field emission transistorof claim 1 wherein the carbon nanotubes extend along the substrate incantilevered fashion prior to reaching the free space region.
 11. Thefield emission transistor of claim 1 further wherein a second pluralityof carbon nanotubes in electrical communication with the secondelectrode and extending from the second electrode toward the firstelectrode terminate at the free space region in the separation region;and wherein electrons may be transmitted between the first and secondelectrodes by means of electrical conduction from the first electrodethrough the first plurality of carbon nanotubes and by field emissionsfrom the first plurality of carbon nanotubes to the second plurality ofcarbon nanotubes and by electrical conduction from the second pluralityof carbon nanotubes to the second electrode; whereby the field emissionsarc between ends of the first plurality of carbon nanotubes and secondplurality of carbon nanotubes.
 12. A method of fabricating a fieldemission transistor comprising: applying a plurality of carbon nanotubesto an insulating surface of a substrate; etching a gap in the carbonnanotubes to define a free space region; applying a first electrode tothe substrate in electrical communication with the carbon nanotubes onone side of the free space region; applying a second electrode to thesubstrate separated from the carbon nanotubes in communication with thefirst electrode by the free space region; applying a gate electrode tothe substrate positioned to establish a controlling electrical fieldwithin the free space region; and transmitting electrons between thefirst and second electrodes by a combination of electrical conductionthrough the plurality of carbon nanotubes and field emissions in thefree space region, the latter controllable by the gate electrode. 13.The method of claim 12 wherein the plurality of carbon nanotubes areprefabricated and then applied in a thin layer to the insulating surfaceto be oriented to extend in a substantially parallel fashion between thefirst and second electrodes.
 14. The method of claim 12 wherein theetching of the gap provides a free space region for each of theplurality of carbon nanotubes that is substantially identical.
 15. Themethod of claim 12 wherein the first electrode is a metal layer appliedto the substrate over pre-applied carbon nanotubes.
 16. The method ofclaim 12 further including the step of applying a negative voltage tothe first electrode with respect to the second electrode for emission ofelectrons from ends of the plurality of carbon nanotubes and controllingcurrent flow between the first and second electrodes by modulating agate voltage on the gate.
 17. The method of claim 12 wherein the voltagebetween the first and second electrodes is less than 50 volts.